Question: Simplify the following expression: $ x = \dfrac{1}{9} - \dfrac{a - 1}{-7a} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-7a}{-7a}$ $ \dfrac{1}{9} \times \dfrac{-7a}{-7a} = \dfrac{-7a}{-63a} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{a - 1}{-7a} \times \dfrac{9}{9} = \dfrac{9a - 9}{-63a} $ Therefore $ x = \dfrac{-7a}{-63a} - \dfrac{9a - 9}{-63a} $ Now the expressions have the same denominator we can simply subtract the numerators: $x = \dfrac{-7a - (9a - 9) }{-63a} $ Distribute the negative sign: $x = \dfrac{-7a - 9a + 9}{-63a}$ $x = \dfrac{-16a + 9}{-63a}$ Simplify the expression by dividing the numerator and denominator by -1: $x = \dfrac{16a - 9}{63a}$